Question: Simplify the expression. $(5z^{3}+5z)(4z^{3}-5z^{2}-7z)$
Solution: First use the distributive property. $ 5 z^3 (4 z^3) + 5 z^3 (-5 z^2) + 5 z^3 (-7 z) + 5 z (4 z^3) + 5 z (-5 z^2) + 5 z (-7 z) $ Simplify. $ 20z^{6} - 25z^{5} - 35z^{4} + 20z^{4} - 25z^{3} - 35z^{2} $ $20z^{6}-25z^{5}-15z^{4}-25z^{3}-35z^{2}$ Identify like terms. $ { 20z^{6}} {- 25z^{5}} {- 35z^{4}} {+ 20z^{4}} {- 25z^{3}} {- 35z^{2}} $ Add the coefficients. $ { 20z^{6}} { -25z^{5}} { -15z^{4}} { -25z^{3}} { -35z^{2}} $